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(Solved): Consider the following network. With the indicated link costs, use Dijkstra's shortest-path algorit ...
Consider the following network. With the indicated link costs, use Dijkstra's shortest-path algorithm to compute the shortest path from node to node . A. Show how the algorithm works by computing the table shown below. Note on answer format: - Fill in the set with selected nodes without space. For example, if the node set contains nodes, , and , enter in the blank. - Fill in the (.) cell without space, for example, for .5 and . in the blank. - When the distance is infinity, write in the abbreviation inf in the blank. - When there is a tie in node distances, please choose from left to right, i.e. the node in the left column is chosen first. B. Enumerate the shortest paths from to . Enter only one node name, , or , into each of the intermediate node cells. Give the total path cost of to in the last cell.
Expert Answer
The algorithm for Dijkstra's shortest path algorithm:Create a function that takes a graph, a source node, and a destination node as inputs.Initialize a list called "distances" to store the tentative distances from the source node to all other nodes in the graph. Set the distance of the source node to 0 and all other nodes to infinity.Initialize a list called "visited" to keep track of the visited nodes. Set all nodes as unvisited initially.While the destination node is not visited: a. Select the unvisited node with the smallest tentative distance and mark it as the current node. b. Mark the current node as visited. c. For each neighboring node of the current node: i. Calculate the tentative distance from the source node to the neighboring node by summing the current node's distance and the weight of the edge between them. ii. If the tentative distance is smaller than the previously recorded distance for the neighboring node, update the distance with the new value.Once the destination node is visited, the algorithm terminates. The shortest path from the source to the destination can be reconstructed by backtracking from the destination node to the source node, following the path with the lowest total distance from the source.